Math calculators

Exponents and logarithms

Log in any base, natural log, log10, powers, nth roots and solving exponential equations a^x = y.

Inputs

xBase b

Results

Methodology

Conventions

Logarithms need x > 0 and a positive base other than 1. Roots of negative numbers are real only for odd n.

References

NIST Digital Library of Mathematical Functions, dlmf.nist.gov, ch. 4

Formulas

Change of base: \log_b x = \frac{\ln x}{\ln b}
nth root: \sqrt[n]{x} = x^{1/n}
Solve for the exponent: b^x = y \iff x = \frac{\ln y}{\ln b}